Nearly isochoric elastic deformations: volume changes in plane strain

Abstract

Plane deformations of nearly incompressible elastic solids are examined with a view to calculating the volume changes accompanying an arbitrary (plane) deformation. The dilatation is shown to be determined from a knowledge of the deformation appropriate to the corresponding incompressible material under the same boundary conditions. This work parallels that given in a previous paper for three-dimensional deformations and relies on the decomposition of the deformation gradient into its dilatational and isochoric parts.